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% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
\title{Zone-based Spectrum Sensing In Cognitive Radio}


\IEEEoverridecommandlockouts
\author{
\IEEEauthorblockN{
    Bilal Acar\IEEEauthorrefmark{2},
    Mehmet Akif Ersoy\IEEEauthorrefmark{2}\thanks{\IEEEauthorrefmark{2}This work has been conducted as the BS graduation project of Bilal Acar and Mehmet Akif Ersoy in the Department of Computer Engineering at Bogazici University},
    H. Birkan Yilmaz,
    Salim Eryigit, and
    Tuna Tugcu
} \IEEEauthorblockA{
Department of Computer Engineering\\ Bogazici University\\ 34342, Bebek, Istanbul, Turkey\\
Email: \{bilal.acar, mehmet.ersoy, birkan.yilmaz, eryigit,
tugcu\}@boun.edu.tr} }




% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}




% make the title area
\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}
%\boldmath
Dynamic access to spectrum requires detecting the free spaces in close proximity. Since non-cooperative sensing methods cannot satisfy most of the basic requirements, different cooperative sensing algorithms have been proposed to overcome this problem. In the previous works, multiple secondary users cooperate to achieve better primary user detection. However, taking into account the measurements from distant users actually aggravates the detection decision. In this paper, we propose the \textbf{\textit{Zone-based Sensing (ZoneS)}} method, which is a distributed cooperative sensing method that circumvents the problems that arise from the cooperation between distant nodes. The simulations are performed with different parameters and with majority cooperation rule for the users in each zone. The false alarm, missed detection, blocking and dropping probabilities, and channel utilization are examined to assess the effectiveness of ZoneS. The proposed method enables the utilization of spectrum bands that would be left unused otherwise, while keeping the probabilities of missed detection and false alarm bounded. Furthermore, the coordination among secondary users is achieved without any overhead.
\end{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\IEEEpeerreviewmaketitle



\section{Introduction}
To improve spectrum utilization, opportunistic spectrum access has been proposed wherein devices occupy the spectrum that has been left vacant. The essential part of opportunistic access is finding the free spaces of the spectrum via spectrum sensing. This includes sensing unused spectrum as well as sensing during the \emph{Cognitive Radio} operation periodically for vacating the channel if primary activity is observed. Cooperative sensing and acquiring processing gain have been studied extensively as a promising alternative to improve the sensing performance in low SNR conditions \cite{ganesan2005css, kattepur2007data, quan2008spatial, quan2009optimal, unnikrishnan2008csp, aysal2008cooperative}.

We mainly focus on energy detection and distributed cooperative sensing issues to increase the performance of the energy detection method under low SNR conditions \cite{sensingReview2011}. Local sensors individually sense the channels and then send information to the network center where the final decision is made\cite{crSensingCDMA2010}. However, the distance between the cooperating nodes is crucial since the cooperation of distant nodes can increase false alarm or missed detection rates. For example, when there is a \textit{Primary User (PU)} at the edge of the cell, the \textit{Secondary Users (SU)} in the opposite part of the cell may not detect its presence. So, the frequency used by this PU may be decided as idle. If this frequency is assigned to a SU in the close proximity of this PU, this situation will result in collision.

In this paper, we propose the \textit{Zone-based Sensing (ZoneS)} method, which is a distributed cooperative sensing method that circumvents the problems that arise from the cooperation between distant nodes. In this method, we divide the secondary cell into several zones with approximately equal areas and each zone decides whether a frequency is idle or not within its area by fusing the sensing results of the SUs in that zone. Since the zones are much smaller than the cell, the cooperation between the SUs in a zone does not cause a problem as in the case of cooperation in the whole cell. Yet, the same frequency may be assigned to other zones in the cell to make sure that it is sensed at different parts of the cell. We examine the ZoneS method and simulate with different number of SUs. We analyze the performance of ZoneS in terms of false alarm, missed detection, collision blocking and dropping probabilities, and utilization. Performance loss is observed in the case of missed detection due to increasing interference level to PUs. On the other hand, in the case of false alarm SUs waste available spectrum holes which, again, causes performance loss \cite{parameterOptimization}.

The rest of the paper is organized as follows: In Section~\ref{sec:system_model}, we overview the general channel model, individual and cooperative sensing of the SUs, and sensing algorithm used in simulation. In Section~\ref{sec:results} we present results of the simulation for different number of SUs. We reveal the conclusion in Section~\ref{sec:conclusion}. Finally, in Section~\ref{sec:future} we state future work to optimize the results.
\section{\label{sec:system_model}System Model}

\subsection{Channel Model}
For the transmission channel, we adopt the path loss channel model described in \cite{faramir}, which includes log-normal shadowing. According to this model the received power of a node, which is $d$ km away from the transmitter, is obtained according to\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\beqn
    P_{rx} = P_{tx} - l_0 - 10\,\, \alpha \,\, log(d) + s(\mu_s, \sigma_s)
\eeqn
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
where $l_0$ is the path loss correction constant, $\alpha$ is the path loss exponent, $s$ is a Gaussian random variate,  $P_{rx}$ and $P_{tx}$ are the receive and transmit powers, respectively.

When there is no transmitter using the sensed channel, the received power is generated by a Gaussian random variate with mean $\mu_0$ (noise floor), and standard deviation $\sigma_0$ (noise deviation).

\subsection{Zone Structure}

\begin{figure}[!htb]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/cellStructure.eps}
\caption{Example zone structure.} \label{fig:zone_structure}
\end{figure}

In Figure~\ref{fig:zone_structure}, the zone structure of an infrastructure based \CR cell is depicted. We assume the \CR cells are sectorized as in general practice. We further divide each sector into radial slices, and divide each slice into zones according to the distance from the base station. Each slice corresponds to an angle of $\beta$, and the radius ($r_1$, $r_2$, etc.) forms the zone structure. Thus, $(\beta, \, r_1, \, ... \, r_n)$ tuple defines the zones in the secondary cell.

Cooperation among all SUs in the secondary cell does not improve, even worsens, the overall performance. Considering all local decisions in case of an active transmission at the edge of the cell may forbid the use of the frequency all over the cell. Similarly, considering all local decisions may result in missed detection in the close proximity of primary transmission. Therefore, we divide the cell into zones where local cooperation leads to better overall performance in terms of false alarm, missed detection, and utilization.

After waiting for a random duration at the end of the silent period, each SU broadcasts its sensing measurement with low power. An SU that has not heard from any of its neighbors before its own transmission considers itself as the leader of its neighborhood. \textbf{Thus, the selection of the leader of a neighborhood is achieved without any messaging overhead.} Since the leader can hear all SUs in its neighborhood, it receives the spectrum sensing measurements of those users. Only the leader reports its neigborhoods sensing decision to the \CR base station. \textbf{Hence, the bandwidth requirement of the report channel is minimized.}

Since the sensing results are reported for each zone separately, the \CR base station can keep track of available frequencies for each zone. A frequency can be determined as available or unavailable in different zones. So, \textbf{the \CR system can utilize even the frequencies, which would be unavailable according to other approaches, in the zones distant to the PU}.

\subsection{ZoneS Sensing Decision}
After sensing the signal powers locally, the SUs compare the received power with the power threshold and decide whether the channel is available or not. At that point, the decision that there is no transmission in a channel while a primary user is actually communicating is called missed detection. On the contrary, the decision that there is an ongoing transmission while no primary user is actually communicating is called false alarm. Probabilities of these occasions give the sensing reliability and sensing efficiency, respectively \cite{UpToDateSensing}. Therefore, the individual false alarm probability of a SU ($\probflocal$) becomes the probability of noise power being greater than the power threshold, and the individual missed detection probability of a SU ($\probmlocal$) becomes the received power being less than the power threshold. This situation is shown in Figure \ref{fig:h0h1}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!htb]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/h0_h1.eps}
\caption{Received Power Distributions.}
\label{fig:h0h1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

After each group leader transmits the local sensing decisions, the \CR base station gathers sensing decisions zone by zone and applies the cooperation rule in each zone. Using majority logic as the cooperation rule yields false alarm probability ($\probf$) and missed detection probability ($\probm$) according to the following formulations:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{equation}
    \begin{array}{lcl}
        \probf & = & \sum\limits_{ k > \frac{N}{2}}^N {N \choose k}(\probflocal)^k(1-\probflocal)^{N-k} \\
        \probm & = & \sum\limits_{ k > \frac{N}{2}}^N {N \choose k}(\probmlocal)^k(1-\probmlocal)^{N-k}
    \end{array}
\end{equation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

ZoneS algorithm divides the cell into zones for efficient cooperation. \textbf{These final $\probf$ and $\probm$ values are the probabilities for a single zone, not the whole cell.}

\subsection{Communication}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!h]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/frameStructure.eps}
\caption{Communication frame structure.} \label{fig:frame_structure}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The communication frame structure is depicted in Figure~\ref{fig:frame_structure}. Each frame starts with sensing scheduling and sensing slots. A simple sensing scheduling method, which assigns half of the frequencies to one half of the nodes in the zone and the other half to the remaining nodes, is assumed. Collaborative sensing decision is formed and acknowledged after these slots. Sensing schedule advertisement, slots, and result acknowledgement are followed by data slot requests and assignments.

\begin{figure}[!ht]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/communicationCases.eps}
\caption{Secondary communication.} \label{fig:network}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

After the sensing part is completed, \CR base station assigns communication frequencies to the SUs who want to receive or transmit data. While choosing which frequencies to assign, it takes the sensing results into consideration. It can assign a frequency to a user in three cases:
\begin{enumerate}
\item No PU is actually using the channel.
\item There is a PU who uses the channel, but it is not close enough to the SU who uses the same channel so that there is not significant interference to the PU.
\item There is a PU close by who uses the channel, but SUs could not detect it (missed detection). This situation causes interference at PU and therefore collision.
\end{enumerate}

These cases are illustrated in Figure \ref{fig:network}. In the figure, there is a secondary link between $SU_A$ and the \CR base station over $f_1$, which is not used by any primary user. Therefore, $SU_A$ can communicate with the \CR base station over $f_1$ safely. There is another secondary link between $SU_B$ and the \CR base station over $f_2$, which is used by $PU_B$ at the other side of the cell. Therefore, the use of $f_2$ does not cause significant interference at $PU_B$. Lastly, there is a secondary link between $SU_C$ and the \CR base station uses $f_3$, which is also used by $PU_C$ in close proximity. In this case, collision occurs due to the missed detection and the channel capacity reduces significantly, hindering a valid communication. In each case the channel capacities are evaluated by the Shannon capacity formula.

\section{\label{sec:results}Results}
\subsection{Simulation Parameters and Analysis}

\begin{table}[!htb]
\renewcommand{\arraystretch}{1.2}
\caption{Simulation Parameters}
\label{tbl:sim_parameters}
\centering
\begin{tabular}{l c l}
  \hline
  Parameter & & Value\\
  \hline
  $P_{tx}$ & & -10 dB \\
  $l_0$    & & 38.4 dB (Urban) \\
  $\alpha$ & & 3.5 (Urban)\\
  $\mu_s$  & & 0 dB\\
  $\sigma_s$ & & 8 dB\\
  $\mu_0$  & & -85 dB \\
  $\sigma_0$ & & 20 dB \\
  $r_{cell}$ & & 1.5 km\\
  $N_{PU}$ & & 1500\\
  \hline
\end{tabular}
\end{table}

Simulation parameters are shown in Table~\ref{tbl:sim_parameters} where $N_{PU}$ stands for the number of PUs. In the simulations, statistics are collected in terms of false alarm, missed detection, collision, blocking of SUs, dropping of SUs, and channel utilization by both SUs and PUs. The reader should note that we do not plot all probability values for each zone. Instead, we plot their mean against the number of SUs.

In the simulations, radius of the \CR cell is taken as 1.5 km, and the number of PUs is 1500. Also, the PUs are deployed in a wider area than the SUs. They are deployed in a circle with approximately 5 km radius since a PU outside of this area cannot be sensed by SUs for the given simulation parameters.

\begin{figure}[b]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/pf.eps}
\caption{Probability of False Alarm vs Number of SUs.}
\label{fig:probf}
\end{figure}

\subsection{$\probf$ Analysis}
Figure \ref{fig:probf} illustrates the false alarm probability against the number of SUs in the cell for no zone (single zone) and 36 zones cases. The probability of false alarm decreases with the increasing number of SUs in the 36 zones case because the reliability of the cooperation decision increases with number of users cooperating. This result is expected according to the mathematical model since the cooperative false alarm probability is obtained by taking powers of local false alarm probabilities. However, with increasing number of SUs in the no zone case  $\probf$ does not change much since there are already too many users cooperating. Although the false alarm probability for the 36 zones case is higher than that of the no zone case, it is still well below the 0.10 bound defined by the standard \cite{wranstandard}.

\begin{figure}[b]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/pm_c.eps}
\caption{Probabilities of Missed Detection and Collision vs Number of
SUs} \label{fig:probm}
\end{figure}

\subsection{$\probm$ and $\mathbf{P_C}$ Analysis}
Figure \ref{fig:probm} illustrates the missed detection and collision probabilities against the number of SUs in the cell for no zone and 36 zones cases. We observe that, in 36 zones case, the probability of the missed detection also decreases with increasing number of SUs as in the same manner for the probability of false alarm. We also observe that collision probabilities ($\mathbf{P_C}$) never exceed the miss-detection probabilities. This is an expected result since all collisions are caused due to missed detections. Another observation from the figure is that, after some point, $\mathbf{P_C}$ starts increasing. That is why the system gets overloaded at that point. However, in the no zone case, these probabilities again remains still with increasing number of SUs such that $\probm$ remains above 0.20 and $\mathbf{P_C}$ remains above 0.10 all the time. This is why, in the no zone case, for the proper detection, the PU should cause interference at least half of the SUs. Otherwise, although the closer SUs to the PU realize that the frequency is not available, due to cooperation the overall decision will be for the availability of the frequency, resulting in a missed detection and a probable collision. Therefore, applying cooperation across the cell increases the probabilities of both miss detection and collision.

\begin{figure}[t]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/pb_d.eps}
\caption{Probabilities of Blocking and Dropping vs Number of SUs}
\label{fig:probb}
\end{figure}

\subsection{Blocking and Dropping Analysis}
Figure \ref{fig:probb} illustrates the blocking and dropping probabilities against number of SUs in the cell. The dropping probability of no zone case is lower than 36 zones due to greater $\probm$ and $\mathbf{P_C}$ of the no zone case. Since $\probm$ and $\mathbf{P_C}$ are higher for the no zone case, the SUs do not detect the collision. Therefore, they do not try to vacate the communication frequency they use, resulting in fewer drops than 36 zones case. On the other hand, blocking probability of no zone case is higher than 36 zones case. This situation occurs since in the 36 zones case, \CR base station can decide that some frequencies are available in some zones. However, in the no zone case the \CR base station decides for the whole cell. As a result, if a frequency is not available for half of the cell, it is  not used in the entire cell. This situation causes \CR users to find less spectrum holes to initiate a communication and increases their blocking probability.

\subsection{Utilization Analysis}
Figure \ref{fig:util} illustrates the utilization of PUs and SUs with respect to the number of SUs in the cell for the no zone and the 36 zones cases. In both cases, SUs utilize the spectrum almost equally. However, in the no zone case, SUs harm primary communication due to the high $\probm$ and $\mathbf{P_C}$ values. Note that the total utilization of PUs and SUs can exceed 100\% because they can use the same frequency simultaneously if they are far enough to experience limited interference which leads no collision. 

\begin{figure}[t]
\centering
\includegraphics[width=0.99\columnwidth,keepaspectratio] {figs/util.eps}
\caption{Utilization of Wireless Channel} \label{fig:util}
\end{figure}

\section{\label{sec:conclusion}Conclusion}
In this paper, we focus on distributed cooperative sensing with majority cooperation rule using the ZoneS approach. We observe that with a few SUs (350 or less), the 0.10 upper bound for false alarm and missed detection probabilities set by the standards cannot be satisfied \cite{wranstandard}. As the number of SUs increases, these requirements can be easily satisfiable, but when the system load becomes excessive (SU utilization over 50\%) quality of service for SUs decreases severely in terms of blocking and dropping. Moreover, due to overload in wireless channel, the collision probabilities start to increase after that point.

We also compare our results with cooperation over the whole cell case (no zone case) and observe that applying cooperation with multiple zones results in better cooperation in terms of sensing reliability since with the multiple zones cooperating in a cell, both missed detection and collision probabilities decrease significantly.

\section{\label{sec:future}Future Work}
As further improvement, we plan to combine our simulation with an optimization approach over sensing scheduling. Our aim at this optimization is to minimize the interference caused by the secondary users by efficiently assigning the frequencies to be sensed for each secondary user.

\section*{Acknowledgement}
This work has been supported by the State Planning Organization (DPT) of Republic of Turkey under the project TAM with the Project No. 2007K120610 and COST Action IC0902 Cognitive Radio and Networking for Cooperative Coexistence of Heterogeneous Wireless Networks.

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